On the persistence of elliptic lower-dimensional tori in Hamiltonian systems under the first Melnikov condition and Rüssmann's non-degeneracy condition

DOI10.1016/J.NA.2006.02.018zbMath1114.37033OpenAlexW2008680720MaRDI QIDQ875274

Dongfeng Zhang, Shaoping Wang, Junxiang Xu

Publication date: 13 April 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.02.018

zbMATH Keywords

non-degeneracy conditionnon-resonance conditionsKAM-iterationnearly integrable analytic Hamiltonian systems

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (2)

Gevrey-smoothness of elliptic lower dimensional invariant tori in Hamiltonian systems ⋮ A KAM theorem for a class of nearly integrable symplectic mappings

Cites Work

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• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
• On elliptic lower dimensional tori in Hamiltonian systems
• Existence of KAM tori in degenerate Hamiltonian systems
• On Melnikov's persistency problem
• Invariant tori of Hamiltonian systems that are nondegenerate in Rüssmann's sense
• Invariant tori for nearly integrable Hamiltonian systems with degeneracy
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• Persistence of lower-dimensional tori under the first Melnikov's non-resonance condition
• PERTURBATION OF QUASIPERIODIC SOLUTIONS OF INFINITE-DIMENSIONAL HAMILTONIAN SYSTEMS

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